A construction task

Give an economic setting for a position with the
following property.

Black is losing. He is allowed to add any material of any color (no K)
and make any series moves (as long as this is legal by the usual
fairy conventions, e.g. as soon as he is checking White, White has the move)
in any order, but he is still lost.

Cheapskate try:

(= 2+21 )

I doubt you can do it in a legal position but surely you can improve my position.
(But not by dropping the Pd2 - think :-)

And I hope you remember that in Rex Multiplex all kings or no king at all can be in check at once.

EDIT: Eh, the last one does not work, seeing now Black can add White material too. So add a queen on e3, gather all kings around it and capture all other White pieces and then the queen. Meh! Just add two more kings to that schema and it should work.

EDIT: Ok, here is a legal setting. Black has no way of winning any pawn by legal means. And looking at your first diagram he does not move with white pieces (or else 1.Bxg4 - 2.Bxf3 - 3.Bg4 - 4.Bh3 f3 5.Bxg2+ fxg2#). So since he can't legally add any Black pieces he has no way of avoiding the loss once White can move. And White CAN move at some point, or else your first diagram is also cooked. :P

Jakob, it is ENTIRELY wrong. The task is to make the most economic position where White has a mate in one, and Black can place any amount of Black and White pieces, minus kings, and can make any series of legal moves, but cannot stop the mate.

In this position, white has a mate in 1, because it's black's move. (see Codex, footnote 19). Without the queen, James would be correct in that it isn't a #1. The pawns can't be left out because of e.g. +bSf7, +bRg7.

"Black is losing" does not mean that there has to be a #1.
Thank you, Joost, I did not think of the cross-check idea. So the black pawns are necessary. And the queen as well, because if the game is over then black is not losing, he has lost.

Sounds legit. (I didn't specify whether Black is in check and even
whether the position itself is legal. Of course I *meant* the last
one, otherwise one could try e.g. illegal double checks. I also
intended Black not to be in check but so there. :-)